Single Photon Emission Computed Tomography (SPECT) reconstructs three dimensional images of radioactive source distributions in the body using a sequence of planar images acquired over a range of angles around the patient.
In order to reconstruct the tomographic image from the set of planar images it is necessary to know the direction from which the photons detected at a given point in the image originated. For X-ray computed tomography (CT), the direction is defined by a line from the anode to the X-ray detector. For Positron Emission Tomography (PET), it is a line between the pair of detectors in which the two coincident 511 keV photons are detected. In SPECT, the direction is usually defined by a collimator—a lead plate with 20,000 to 50,000 small holes formed in it which restricts the detected incident photons to only those with known angles of incidence at the detector.
The most popular collimator type is the parallel beam collimator, in which the holes are designed to point perpendicular to the detector surface. Another type of collimator is referred to as a fan beam collimator. With the fan beam collimator, the holes in one dimension (transverse) focus to a point; there is no focusing in the axial dimension. A further type of collimator is referred to as a cone beam collimator. The cone beam collimator focuses to a single point in both transverse and axial dimensions.
Reconstruction algorithms in the current state of the art assume that the construction of these collimators is perfect. Such algorithms perform back projection of planar projection data and forward projections of the object estimates under this assumption. In reality, however, collimators are not perfect. Their construction is subject to dimensional errors such that all holes do not point in the ideal intended direction. This leads to errors in forward and backward projections and, results in distortions and degradation of the resolution in the final tomographic images.
Therefore, there is a need for an improved method for accounting for inaccuracies in the collimator hole pointing directions, and for employing this accounting in the reconstruction process to remove distortions and improve the resolution of reconstructed images.